关于2表为不同奇单位分数的和

On Expressing Two as Sums of Distinct Odd Unit Fractions

记m=33×5×7×11×13×17×19×23×29×31×37,本文得到2的不同奇单位分数之和的分解式:2=1/3+1/5+1/7+1/9+1/(11)+1/(13)+1/(15)+1/(17)+1/(19)+1/(21)+1/(27)+1/(29)+…+1/(954 094 903 047)。式中共有4 074个奇单位分数,单位分数的分母分别为m的除了1,23,3×11×29,3×11×23×29×37,3×13×17×19×23×29×37,m/(51),m/(33),m/(31),m/(29),m/(27),m/(23),m/(21),m/(19),m/(17),m/(15),m/(13),m/(11),m/9,m/7,m/5,m/3,m共22个因数之外的其余全部因数,最大分母为m35。

Abstract： By denoting m = 3^3 x5 x7 x 11 x 13 x 17 x 19 x23 x29 x31 x37, an expression of two as a sum of distinct odd unit fractions： 2=1/3＋1/5＋1/7＋1/9＋1/（11）＋1/（13）＋1/（15）＋1/（17）＋1/（19）＋1/（21）＋1/（27）＋1/（29）＋…＋1/（954 094 903 047） is obtained. There are 4074 odd unit fractions in the expansion. The denominators of unit 954 094 903 047 fractions are all divisors ofm except for 22 divisors 1,23,3×11×29,3×11×23×29×37,3×13×17×19×23×29×37,m/（51）,m/（33）,m/（31）,m/（29）,m/（27）,m/（23）,m/（21）,m/（19）,m/（17）,m/（15）,m/（13）,m/（11）,m/9,m/7,m/5,m/3,m and the max denominator is m/35.